DOI: 10.1515/jgth-2022-0215 ISSN: 1433-5883
A characterization of finite groups having a single Galois conjugacy class of certain irreducible characters
Yu Zeng, Dongfang Yang Abstract
Let 𝐺 be a finite group and let
Irr
s
(
G
)
\mathrm{Irr}_{\mathfrak{s}}(G)
be the set of irreducible complex characters 𝜒 of 𝐺 such that
χ
(
1
)
2
\chi(1)^{2}
does not divide the index of the kernel of 𝜒.
In this paper, we classify the finite groups 𝐺 for which any two characters in
Irr
s
(
G
)
\mathrm{Irr}_{\mathfrak{s}}(G)
are Galois conjugate.
In particular, we show that such groups are solvable with Fitting height 2.